Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 1657)

Label	Polynomial	Discriminant	Galois group	Class group
36.0.11636034958735032166924075841251447518799351583251569.1	x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21 - x^20 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1	\( 3^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[9]$ (GRH)
36.0.599781089369859106058502013153430001897393515831230464.1	x^36 - x^18 + 1	\( 2^{36}\cdot 3^{90} \)	$C_2\times C_{18}$ (as 36T2)	$[19]$ (GRH)
36.0.2063964752380648518006363619171361060603216996551622656.1	x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1	\( 2^{36}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[19]$ (GRH)
36.0.33294538757658815101209249418169888839879795074462890625.1	x^36 - 76x^27 + 5777x^18 + 76x^9 + 1	\( 3^{90}\cdot 5^{18} \)	$C_2\times C_{18}$ (as 36T2)	$[37]$ (GRH)
36.0.114573059505387793044837364496233492772337802886962890625.1	x^36 - x^35 + 2x^34 - 3x^33 + 5x^32 - 8x^31 + 13x^30 - 21x^29 + 34x^28 - 55x^27 + 89x^26 - 144x^25 + 233x^24 - 377x^23 + 610x^22 - 987x^21 + 1597x^20 - 2584x^19 + 4181x^18 + 2584x^17 + 1597x^16 + 987x^15 + 610x^14 + 377x^13 + 233x^12 + 144x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2x^2 + x + 1	\( 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[76]$ (GRH)
36.0.14212734556341031905549296191351828189377245025195450200601.1	x^36 - 5x^27 - 487x^18 - 2560x^9 + 262144	\( 3^{90}\cdot 7^{18} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.48908816365067043970916287981601635325839249495639564072729.1	x^36 - x^35 - x^34 + 3x^33 - x^32 - 5x^31 + 7x^30 + 3x^29 - 17x^28 + 11x^27 + 23x^26 - 45x^25 - x^24 + 91x^23 - 89x^22 - 93x^21 + 271x^20 - 85x^19 - 457x^18 - 170x^17 + 1084x^16 - 744x^15 - 1424x^14 + 2912x^13 - 64x^12 - 5760x^11 + 5888x^10 + 5632x^9 - 17408x^8 + 6144x^7 + 28672x^6 - 40960x^5 - 16384x^4 + 98304x^3 - 65536x^2 - 131072x + 262144	\( 7^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[2, 74]$ (GRH)
36.0.157229013891772345498599951736092754417390325814062078754816.1	x^36 - 512x^18 + 262144	\( 2^{54}\cdot 3^{90} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.157229013891772345498599951736092754417390325814062078754816.2	x^36 + 512x^18 + 262144	\( 2^{54}\cdot 3^{90} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.541055976048072725104260184584057273870769716344028569534464.1	x^36 - 2x^34 + 4x^32 - 8x^30 + 16x^28 - 32x^26 + 64x^24 - 128x^22 + 256x^20 - 512x^18 + 1024x^16 - 2048x^14 + 4096x^12 - 8192x^10 + 16384x^8 - 32768x^6 + 65536x^4 - 131072x^2 + 262144	\( 2^{54}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.541055976048072725104260184584057273870769716344028569534464.2	x^36 + 2x^34 + 4x^32 + 8x^30 + 16x^28 + 32x^26 + 64x^24 + 128x^22 + 256x^20 + 512x^18 + 1024x^16 + 2048x^14 + 4096x^12 + 8192x^10 + 16384x^8 + 32768x^6 + 65536x^4 + 131072x^2 + 262144	\( 2^{54}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.2215020037800761116296816339199940379209022060324490202578944.1	x^36 - 17x^34 + 169x^32 - 1130x^30 + 5664x^28 - 21853x^26 + 66874x^24 - 162613x^22 + 316711x^20 - 487810x^18 + 592078x^16 - 549123x^14 + 384931x^12 - 190091x^10 + 66033x^8 - 13002x^6 + 1695x^4 - 45x^2 + 1	\( 2^{36}\cdot 3^{18}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	$[171]$ (GRH)
36.0.48526755753740305052512669329205843844959387036328330042655969.1	x^36 - 136x^27 - 1187x^18 - 2676888x^9 + 387420489	\( 3^{90}\cdot 11^{18} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.80731161945559438248836517604483794680492496928434000672170721.1	x^36 - x^35 + 18x^34 - 15x^33 + 185x^32 - 137x^31 + 1281x^30 - 831x^29 + 6616x^28 - 3799x^27 + 26339x^26 - 13196x^25 + 83006x^24 - 36260x^23 + 208286x^22 - 77735x^21 + 418163x^20 - 132518x^19 + 666068x^18 - 173318x^17 + 834766x^16 - 177139x^15 + 804267x^14 - 129870x^13 + 582511x^12 - 73129x^11 + 302060x^10 - 23507x^9 + 107217x^8 - 7128x^7 + 23244x^6 - 78x^5 + 2775x^4 - 165x^3 + 126x^2 + 9x + 1	\( 3^{18}\cdot 37^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[19, 684]$ (GRH)
36.0.122958312298624478991860638998897557972401876087680816650390625.1	x^36 - x^35 + 26x^34 - 15x^33 + 413x^32 - 173x^31 + 4027x^30 - 789x^29 + 28017x^28 - 2298x^27 + 134511x^26 + 7347x^25 + 472642x^24 + 48836x^23 + 1180619x^22 + 171615x^21 + 2210278x^20 + 335012x^19 + 3064502x^18 + 471070x^17 + 3227734x^16 + 424487x^15 + 2498777x^14 + 259210x^13 + 1437594x^12 + 75846x^11 + 567447x^10 - 2642x^9 + 158238x^8 - 9682x^7 + 24598x^6 - 3269x^5 + 2670x^4 - 215x^3 + 80x^2 + 5x + 1	\( 3^{18}\cdot 5^{18}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	$[9, 1629]$ (GRH)
36.0.166990115557548038315544519372094023948173088869511853538488801.1	x^36 - x^35 - 2x^34 + 5x^33 + x^32 - 16x^31 + 13x^30 + 35x^29 - 74x^28 - 31x^27 + 253x^26 - 160x^25 - 599x^24 + 1079x^23 + 718x^22 - 3955x^21 + 1801x^20 + 10064x^19 - 15467x^18 + 30192x^17 + 16209x^16 - 106785x^15 + 58158x^14 + 262197x^13 - 436671x^12 - 349920x^11 + 1659933x^10 - 610173x^9 - 4369626x^8 + 6200145x^7 + 6908733x^6 - 25509168x^5 + 4782969x^4 + 71744535x^3 - 86093442x^2 - 129140163x + 387420489	\( 11^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.392893567271872510941083606170645734076396278452324169894854656.1	x^36 + 49x^32 + 932x^28 + 8695x^24 + 41461x^20 + 96055x^16 + 93536x^12 + 28314x^8 + 1365x^4 + 1	\( 2^{72}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	$[19, 171]$ (GRH)
36.36.799622233646074762983150698451178476894456963777140963130998784.1	x^36 - 35x^34 + 560x^32 - 5426x^30 + 35554x^28 - 166634x^26 + 576201x^24 - 1494747x^22 + 2929464x^20 - 4334718x^18 + 4805781x^16 - 3932287x^14 + 2318239x^12 - 949739x^10 + 256105x^8 - 41769x^6 + 3570x^4 - 120x^2 + 1	\( 2^{36}\cdot 3^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.799622233646074762983150698451178476894456963777140963130998784.1	x^36 + 37x^34 + 628x^32 + 6478x^30 + 45354x^28 + 227942x^26 + 848161x^24 + 2375189x^22 + 5038516x^20 + 8084594x^18 + 9725341x^16 + 8624289x^14 + 5490811x^12 + 2413645x^10 + 691677x^8 + 118407x^6 + 10470x^4 + 360x^2 + 1	\( 2^{36}\cdot 3^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[52934]$ (GRH)
36.0.799622233646074762983150698451178476894456963777140963130998784.2	x^36 + 19x^34 + 209x^32 + 1558x^30 + 8740x^28 + 38095x^26 + 132810x^24 + 372723x^22 + 848787x^20 + 1558038x^18 + 2298126x^16 + 2670317x^14 + 2415451x^12 + 1629193x^10 + 806113x^8 + 262086x^6 + 57399x^4 + 5415x^2 + 361	\( 2^{36}\cdot 3^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.799622233646074762983150698451178476894456963777140963130998784.3	x^36 + 3x^34 + 9x^32 + 27x^30 + 81x^28 + 243x^26 + 729x^24 + 2187x^22 + 6561x^20 + 19683x^18 + 59049x^16 + 177147x^14 + 531441x^12 + 1594323x^10 + 4782969x^8 + 14348907x^6 + 43046721x^4 + 129140163x^2 + 387420489	\( 2^{36}\cdot 3^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.981506694911161790066526032030527389205087841773474128847803921.1	x^36 - 1810x^27 + 3295783x^18 + 35626230x^9 + 387420489	\( 3^{90}\cdot 13^{18} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.3377557676335881126900903346326957671873387511586368229584565009.1	x^36 - x^35 + 4x^34 - 7x^33 + 19x^32 - 40x^31 + 97x^30 - 217x^29 + 508x^28 - 1159x^27 + 2683x^26 - 6160x^25 + 14209x^24 - 32689x^23 + 75316x^22 - 173383x^21 + 399331x^20 - 919480x^19 + 2117473x^18 + 2758440x^17 + 3593979x^16 + 4681341x^15 + 6100596x^14 + 7943427x^13 + 10358361x^12 + 13471920x^11 + 17603163x^10 + 22812597x^9 + 29996892x^8 + 38440899x^7 + 51549777x^6 + 63772920x^5 + 90876411x^4 + 100442349x^3 + 172186884x^2 + 129140163x + 387420489	\( 13^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.4579626957516085526487220638656255445999152174466832174789165056.1	x^36 + 54x^32 + 1143x^28 + 12006x^24 + 65367x^20 + 175806x^16 + 203838x^12 + 70632x^8 + 5481x^4 + 1	\( 2^{72}\cdot 3^{88} \)	$C_2\times C_{18}$ (as 36T2)	$[6327]$ (GRH)
36.0.14319849782617254182563766395402434634362109577782479558283362304.1	x^36 + 35x^34 + 561x^32 + 5456x^30 + 35960x^28 + 169911x^26 + 593775x^24 + 1560780x^22 + 3108105x^20 + 4686825x^18 + 5311735x^16 + 4457400x^14 + 2704156x^12 + 1144066x^10 + 319770x^8 + 54264x^6 + 4845x^4 + 171x^2 + 1	\( 2^{36}\cdot 37^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[130473]$ (GRH)
36.0.21809974230617285625493307131308780792777539584000000000000000000.1	x^36 + 51x^34 + 1129x^32 + 14310x^30 + 115592x^28 + 628407x^26 + 2373706x^24 + 6356559x^22 + 12218191x^20 + 16953894x^18 + 16964206x^16 + 12133089x^14 + 6090371x^12 + 2080353x^10 + 460449x^8 + 61182x^6 + 4335x^4 + 135x^2 + 1	\( 2^{36}\cdot 5^{18}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	$[81529]$ (GRH)
36.0.41216642617644769738384985747906299013992369570201489573102485504.1	x^36 + 36x^34 + 594x^32 + 5952x^30 + 40455x^28 + 197316x^26 + 712530x^24 + 1937520x^22 + 3996135x^20 + 6249100x^18 + 7354710x^16 + 6418656x^14 + 4056234x^12 + 1790712x^10 + 523260x^8 + 93024x^6 + 8721x^4 + 324x^2 + 1	\( 2^{72}\cdot 3^{90} \)	$C_2\times C_{18}$ (as 36T2)	$[180486]$ (GRH)
36.36.41216642617644769738384985747906299013992369570201489573102485504.1	x^36 - 36x^34 + 594x^32 - 5952x^30 + 40455x^28 - 197316x^26 + 712530x^24 - 1937520x^22 + 3996135x^20 - 6249100x^18 + 7354710x^16 - 6418656x^14 + 4056234x^12 - 1790712x^10 + 523260x^8 - 93024x^6 + 8721x^4 - 324x^2 + 1	\( 2^{72}\cdot 3^{90} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.41216642617644769738384985747906299013992369570201489573102485504.2	x^36 + 54x^32 + 1143x^28 + 12006x^24 + 65367x^20 + 175878x^16 + 201654x^12 + 77760x^8 + 3321x^4 + 9	\( 2^{72}\cdot 3^{90} \)	$C_2\times C_{18}$ (as 36T2)	$[10298]$ (GRH)
36.36.44387950739803436916061690678602018428037077267652774810791015625.1	x^36 - x^35 - 55x^34 + 54x^33 + 1316x^32 - 1262x^31 - 18056x^30 + 16794x^29 + 157962x^28 - 141168x^27 - 929619x^26 + 788451x^25 + 3797668x^24 - 3009217x^23 - 10994500x^22 + 7985283x^21 + 22875412x^20 - 14890129x^19 - 34467709x^18 + 19586929x^17 + 37621312x^16 - 18102232x^15 - 29492311x^14 + 11597407x^13 + 16278597x^12 - 5027655x^11 - 6107727x^10 + 1424143x^9 + 1470387x^8 - 252736x^7 - 206783x^6 + 26779x^5 + 14445x^4 - 1460x^3 - 340x^2 + 20x + 1	\( 3^{18}\cdot 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.44387950739803436916061690678602018428037077267652774810791015625.1	x^36 - x^35 + 35x^34 - 31x^33 + 556x^32 - 432x^31 + 5314x^30 - 3586x^29 + 34162x^28 - 19818x^27 + 156466x^26 - 77194x^25 + 527433x^24 - 218657x^23 + 1332275x^22 - 457647x^21 + 2542252x^20 - 711664x^19 + 3665766x^18 - 809761x^17 + 3956632x^16 - 539957x^15 + 3063059x^14 + 517817x^13 + 1345047x^12 + 2800770x^11 - 276502x^10 + 5237843x^9 - 1026513x^8 + 5476374x^7 - 560238x^6 + 2102034x^5 + 267795x^4 + 3047715x^3 - 4108065x^2 - 5418330x + 21850951	\( 3^{18}\cdot 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[247608]$ (GRH)
36.0.44387950739803436916061690678602018428037077267652774810791015625.2	x^36 - x^35 - 19x^34 + 20x^33 + 208x^32 - 228x^31 - 1538x^30 + 1766x^29 + 8512x^28 - 10278x^27 - 36329x^26 + 46607x^25 + 122532x^24 - 169139x^23 - 326116x^22 + 495255x^21 + 679648x^20 - 1174903x^19 - 1062783x^18 + 2247035x^17 + 1113874x^16 - 3183278x^15 - 600913x^14 + 942095x^13 + 2074269x^12 + 3200721x^11 - 6904183x^10 + 19867883x^9 - 12157587x^8 - 58512762x^7 + 70408263x^6 + 11551791x^5 - 81902655x^4 + 82074510x^3 - 177270x^2 - 87226170x + 87403801	\( 3^{18}\cdot 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.44387950739803436916061690678602018428037077267652774810791015625.3	x^36 - x^35 - 3x^34 + 7x^33 + 5x^32 - 33x^31 + 13x^30 + 119x^29 - 171x^28 - 305x^27 + 989x^26 + 231x^25 - 4187x^24 + 3263x^23 + 13485x^22 - 26537x^21 - 27403x^20 + 133551x^19 - 23939x^18 + 534204x^17 - 438448x^16 - 1698368x^15 + 3452160x^14 + 3341312x^13 - 17149952x^12 + 3784704x^11 + 64815104x^10 - 79953920x^9 - 179306496x^8 + 499122176x^7 + 218103808x^6 - 2214592512x^5 + 1342177280x^4 + 7516192768x^3 - 12884901888x^2 - 17179869184x + 68719476736	\( 3^{18}\cdot 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.52488303469710461753453989107747724546083978878098845653195292921.1	x^36 - x^35 - 25x^34 + 12x^33 + 338x^32 - 35x^31 - 3596x^30 + 75x^29 + 31599x^28 + 708x^27 - 221058x^26 - 33939x^25 + 1281217x^24 + 260669x^23 - 6307141x^22 - 1034028x^21 + 25482307x^20 + 5036015x^19 - 82683121x^18 - 21277922x^17 + 219610804x^16 + 36478832x^15 - 460870720x^14 - 25242848x^13 + 716973312x^12 + 105430656x^11 - 784816896x^10 - 223400960x^9 + 631394304x^8 + 37050368x^7 - 296185856x^6 + 80846848x^5 + 88227840x^4 - 13107200x^3 - 3604480x^2 - 655360x + 262144	\( 3^{18}\cdot 7^{18}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	$[2, 666]$ (GRH)
36.0.122742088752587853242976134017548025824688225088579999619212332041.1	x^36 - 4693x^27 + 22286393x^18 + 1230241792x^9 + 68719476736	\( 3^{90}\cdot 17^{18} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.36.141834577785145976449731181827603110001579056521289025332042530816.1	x^36 - 36x^34 + 593x^32 - 5920x^30 + 39992x^28 - 193312x^26 + 689479x^24 - 1844392x^22 + 3724921x^20 - 5673268x^18 + 6463399x^16 - 5422832x^14 + 3269436x^12 - 1365584x^10 + 374154x^8 - 61776x^6 + 5325x^4 - 180x^2 + 1	\( 2^{72}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.141834577785145976449731181827603110001579056521289025332042530816.1	x^36 + 36x^34 + 593x^32 + 5920x^30 + 39992x^28 + 193312x^26 + 689479x^24 + 1844392x^22 + 3724921x^20 + 5673268x^18 + 6463399x^16 + 5422832x^14 + 3269436x^12 + 1365584x^10 + 374154x^8 + 61776x^6 + 5325x^4 + 180x^2 + 1	\( 2^{72}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[171, 1026]$ (GRH)
36.0.141834577785145976449731181827603110001579056521289025332042530816.2	x^36 + 57x^32 + 1292x^28 + 14839x^24 + 91181x^20 + 291327x^16 + 436088x^12 + 246202x^8 + 33573x^4 + 361	\( 2^{72}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	$[19, 1026]$ (GRH)
36.0.254220364621420587352541611206660801314202845184000000000000000000.1	x^36 + 54x^34 + 1269x^32 + 17118x^30 + 147510x^28 + 857304x^26 + 3468195x^24 + 9962190x^22 + 20569950x^20 + 30703482x^18 + 33080274x^16 + 25472799x^14 + 13732377x^12 + 5001777x^10 + 1161216x^8 + 156168x^6 + 10341x^4 + 243x^2 + 1	\( 2^{36}\cdot 3^{88}\cdot 5^{18} \)	$C_2\times C_{18}$ (as 36T2)	$[19, 12483]$ (GRH)
36.0.422379680368177798715623889905033676852479341516255339435483316489.1	x^36 - x^35 + 5x^34 - 9x^33 + 29x^32 - 65x^31 + 181x^30 - 441x^29 + 1165x^28 - 2929x^27 + 7589x^26 - 19305x^25 + 49661x^24 - 126881x^23 + 325525x^22 - 833049x^21 + 2135149x^20 - 5467345x^19 + 14007941x^18 + 21869380x^17 + 34162384x^16 + 53315136x^15 + 83334400x^14 + 129926144x^13 + 203411456x^12 + 316293120x^11 + 497352704x^10 + 767819776x^9 + 1221591040x^8 + 1849688064x^7 + 3036676096x^6 + 4362076160x^5 + 7784628224x^4 + 9663676416x^3 + 21474836480x^2 + 17179869184x + 68719476736	\( 17^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.580654212789242722070512622423229170767369878981703159664854695936.1	x^36 - 34x^34 + 676x^32 - 9040x^30 + 90624x^28 - 699296x^26 + 4279936x^24 - 20814464x^22 + 81078016x^20 - 249758720x^18 + 606287872x^16 - 1124603904x^14 + 1576677376x^12 - 1557225472x^10 + 1081884672x^8 - 426049536x^6 + 111083520x^4 - 5898240x^2 + 262144	\( 2^{54}\cdot 3^{18}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.580654212789242722070512622423229170767369878981703159664854695936.2	x^36 + 34x^34 + 676x^32 + 9040x^30 + 90624x^28 + 699296x^26 + 4279936x^24 + 20814464x^22 + 81078016x^20 + 249758720x^18 + 606287872x^16 + 1124603904x^14 + 1576677376x^12 + 1557225472x^10 + 1081884672x^8 + 426049536x^6 + 111083520x^4 + 5898240x^2 + 262144	\( 2^{54}\cdot 3^{18}\cdot 19^{32} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.36.794911346891760916131484470981274061649585725862903171539306640625.1	x^36 - x^35 - 52x^34 + 47x^33 + 1177x^32 - 947x^31 - 15301x^30 + 10771x^29 + 127184x^28 - 76859x^27 - 713805x^26 + 363060x^25 + 2791702x^24 - 1171922x^23 - 7758928x^22 + 2637723x^21 + 15506227x^20 - 4188542x^19 - 22401208x^18 + 4709558x^17 + 23361262x^16 - 3730447x^15 - 17429913x^14 + 2049918x^13 + 9135431x^12 - 759461x^11 - 3261522x^10 + 180587x^9 + 755073x^8 - 24948x^7 - 104688x^6 + 1398x^5 + 7575x^4 + 75x^3 - 216x^2 - 9x + 1	\( 5^{18}\cdot 37^{34} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.908819719841676525092557848566442535650646971382385935623234726609.1	x^36 - 2506x^27 + 4326911x^18 - 4894531250x^9 + 3814697265625	\( 3^{90}\cdot 19^{18} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.0.2287983281592785286172874500859947211827825606656000000000000000000.1	x^36 - 1953125x^18 + 3814697265625	\( 2^{36}\cdot 3^{90}\cdot 5^{18} \)	$C_2\times C_{18}$ (as 36T2)	n/a
36.36.2287983281592785286172874500859947211827825606656000000000000000000.1	x^36 - 54x^34 + 1269x^32 - 17118x^30 + 147510x^28 - 857304x^26 + 3468195x^24 - 9962190x^22 + 20569950x^20 - 30715038x^18 + 33159726x^16 - 25700409x^14 + 14084001x^12 - 5318379x^10 + 1328724x^8 - 206064x^6 + 17901x^4 - 729x^2 + 9	\( 2^{36}\cdot 3^{90}\cdot 5^{18} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.2287983281592785286172874500859947211827825606656000000000000000000.2	x^36 + 36x^34 + 594x^32 + 5952x^30 + 40455x^28 + 197316x^26 + 712530x^24 + 1937520x^22 + 3996135x^20 + 6243322x^18 + 7250706x^16 + 5638626x^14 + 901446x^12 - 5645574x^10 - 9773136x^8 - 7915284x^6 - 3111399x^4 - 467694x^2 + 33373729	\( 2^{36}\cdot 3^{90}\cdot 5^{18} \)	$C_2\times C_{18}$ (as 36T2)	$[923742]$ (GRH)
36.0.2287983281592785286172874500859947211827825606656000000000000000000.3	x^36 - 36x^34 + 594x^32 - 5952x^30 + 40455x^28 - 197316x^26 + 712530x^24 - 1937520x^22 + 3996135x^20 - 6254878x^18 + 7458714x^16 - 7198686x^14 + 7211022x^12 - 9226998x^10 + 10819656x^8 - 8101332x^6 + 3128841x^4 - 468342x^2 + 33396841	\( 2^{36}\cdot 3^{90}\cdot 5^{18} \)	$C_2\times C_{18}$ (as 36T2)	$[1406]$ (GRH)
36.36.7873400697252840110803083874402469866192691789824000000000000000000.1	x^36 - 57x^34 + 1425x^32 - 20634x^30 + 192812x^28 - 1228749x^26 + 5515738x^24 - 17801385x^22 + 41855195x^20 - 72233250x^18 + 91675950x^16 - 85215855x^14 + 57368315x^12 - 27413979x^10 + 9002257x^8 - 1929906x^6 + 248007x^4 - 16245x^2 + 361	\( 2^{36}\cdot 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	Trivial (GRH)
36.0.7873400697252840110803083874402469866192691789824000000000000000000.1	x^36 - 5x^34 + 25x^32 - 125x^30 + 625x^28 - 3125x^26 + 15625x^24 - 78125x^22 + 390625x^20 - 1953125x^18 + 9765625x^16 - 48828125x^14 + 244140625x^12 - 1220703125x^10 + 6103515625x^8 - 30517578125x^6 + 152587890625x^4 - 762939453125x^2 + 3814697265625	\( 2^{36}\cdot 5^{18}\cdot 19^{34} \)	$C_2\times C_{18}$ (as 36T2)	n/a